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Most machine screw fasteners break due to the corrosion that is locking them in the threads. They may be 10-32 but Ford also used 12-24 screws in that time frame.
Heat the screw shank up to over boiling point (250 degrees F) and then quench with water to help break the corrosion up. If that doesn't work the go hotter with it till it finally lets go. Use a needle nose vice grip to grab the shank if possible or weld something to it if possible.
If these are wood screws then that will take a different tack on removal.